Shikaku

Shikaku, sometimes called 'Divide by Box' or 'Divide by Squares' in English, is a Nikoli puzzle in which the aim of the game is to divide a grid into rectangular and square spaces based on the numbers given on the grid. It can be played on any sized grid, but the bigger the grid the harder the puzzle usually becomes. A lot of it does depend on the amount of squares and the placement of the hints however.

The rules are simple:
- Divide the grid into rectangles and squares using the numbers as indicators of how big the rectangle or square has to be.
- Each number must be part of a square or rectangle that is as many cells big as the number itself. So a 2x2 number could cover a 4, for example.
- Each number must be in its own square or rectangle.

Standard version

Shikaku can seem like a difficult puzzle at first. The numbers don't always seem to allow for many deductions, trial and error seems to be a lengthy process for this puzzle, and without knowing any tricks it can indeed be a lengthy process no matter how you go about solving a Shikaku puzzle.
One good starting point is clusters of numbers. The more numbers are together the more paths they're blocking. Since no 2 numbers can be in the same square or rectangle you know their respective rooms cannot go the way of the other numbers, minimizing some of your options, and, in some cases, providing you with a single possible solution.

Another option is to start with the bigger numbers. They often have few places to go due to their size, but in well designed, difficult puzzles their number hints are often placed in such a way that multiple large squares and rectangles fit within the overall space the hint occupies.

Converting it to an RPG setting.

The first thing I saw after looking at a solved Shikaku puzzle was the possibility of turning that solution into a building's layout. Of course this isn't the only possible adaptation you can make, but they do tend to be similarly themed.
The layout of an army camp, lock boxes in a wall, animal enclosures in a zoo, crates of goods stored in a warehouse. There's plenty of opportunities to use a puzzle like this in a campaign, but sometimes it does require a little extra imagination.

To go back to my example of a building's layout, my character (seen below) is given a map with a grid and the numbers on that grid, with the instructions on how to solve a Shikaku puzzle. She also knows it'll give her a rough layout of a building she has to enter as part of her mission. The layout won't contain any details, but merely give her the sizes of all rooms, which will be a tremendous clue in and of itself.

If she doesn't manage to solve the puzzle she'll likely end up confused and lost in the building she has to sneak into. Some of the rooms are only accessible through secret doors, like the 2x2 room with chests in it. Without a map this room could easily be missed, but with the map she'll know there must be a room in that spot.

Obviously she wouldn't know there are chests in that room, in fact she wouldn't even know where the regular doors are (I added those to the image for effect), but if you do want to make it easier for your players you could have the map reveal more details through magic after the puzzle has been solved.
Overall it's a simple enough puzzle to not need magic, but it's also a very effective one in terms of rewarding players for overcoming an optional puzzle. Without the solution they'll still be able to infiltrate the building, find the lock boxes in the wall, figure out the layout of the army camp, and so on, but with the solution everything becomes clearer and easier. A fit reward on its own, but perhaps the solution shows more than just the easy path.